Installing Interior door at bottom of stairs

Hi there

From our main living area/kitchen/hallway, there are 7 steps that lead down to our family room in our side-split home.

About 3 feet from the foot of the stairs, there is an opening for which we'd like to install an interior door, that would be right beside a set of further stairs that lead to the basement. However, there is an additional area above that would be 'empty' just above our proposed new door, and new drywall would need to be installed.

How would I install this drywall? Do I have to frame this area before applying the drywall? It is only about a 2 feet high x 4 feet wide area above the proposed door...I'm a relative novice and want to gather informaiton first...